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(B) The instantaneous power dissipated in a resistor is given by $P = I^2R$. For an alternating current,the root mean square $(RMS)$ current is define

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$\frac{1}{2}I_p^2R$

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(B) The instantaneous power dissipated in a resistor is given by $P = I^2R$. For an alternating current,the root mean square $(RMS)$ current is defined as $I_{rms} = \frac{I_p}{\sqrt{2}}$,where $I_p$ is the peak current. The average power dissipated in the resistor is $P_{avg} = I_{rms}^2 R$. Substituting the value of $I_{rms}$,we get $P_{avg} = \left( \frac{I_p}{\sqrt{2}} \right)^2 R = \frac{I_p^2}{2} R = \frac{1}{2} I_p^2 R$.

The power dissipated in a resistor of resistance $R$ when an alternating current with a peak value of $I_p$ flows through it is:

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